US 20060009963 A1 Abstract Various methods formulated using a geometric interpretation for identifying bilingual pairs in comparable corpora using a bilingual dictionary are disclosed. The methods may be used separately or in combination to compute the similarity between bilingual pairs.
Claims(24) 1. A method for identifying bilingual pairs in comparable corpora using a bilingual dictionary, comprising:
(a) using the comparable corpora to build source context vectors and target context vectors; (b) defining: (i) a source word space with the source context vectors, and (ii) a target word space with the target context vectors; (c) using the bilingual dictionary to project: (i) the source context vectors from the source word space to a source dictionary space, and (ii) the target context vectors from the target word space to a target dictionary space; (d) using the source and target context vectors from the dictionary spaces to identify source/target context vector pairs in a bilingual space; (e) computing a similarity measure for the source/target context vector pairs identified in the bilingual space to identify a bilingual pair. 2. The method according to
pruning components from the context vectors; and normalizing the pruned context vectors. 3. The method according to
building context vectors using entries in the bilingual dictionary; and projecting at (c): (i) the source context vectors and the dictionary entry context vectors from the source word space to a source dictionary space, and (ii) the target context vectors and the dictionary entry context vectors from the target word space to a target dictionary space. 4. The method according to
adding the source/target pairs as entries in the bilingual dictionary; and using the bilingual dictionary to perform one or more of cross-language information retrieval, and cross-language categorization. 5. The method according to
6. The method according to
7. The method according to
8. The method according to
9. The method according to
(v, w)= {right arrow over (v)},{right arrow over (tr(w))} =(P _{s} {right arrow over (v)})^{T} M(P _{t} {right arrow over (w)}), where {right arrow over (v)} is a source context vector; {right arrow over (w)} is a target context vector; P_{s }is a source projection matrix; P_{t }is a target projection matrix; M is a matrix that encodes the relationship between the source and target words s and t in the bilingual dictionary; and {right arrow over (tr(w))} is the translation of the target context vector {right arrow over (w)}. 10. The method according to
11. The method according to
(v, w)= SQ _{s} {right arrow over (v)},TQ _{t} {right arrow over (w)} ={right arrow over (v)} ^{T} Q _{s} ^{T} S ^{T} TQ _{t} {right arrow over (w)}, where {right arrow over (v)} is a source context vector; {right arrow over (w)} is a target context vector; Q_{s }is a projection matrix for mapping the source context vector {right arrow over (v)} on a sub-space generated by ({right arrow over (s_{1})}, . . . , {right arrow over (s_{p})}); Q_{t }is a projection matrix for mapping the target context vector {right arrow over (w)} on a sub-space generated by ({right arrow over (t_{1})}, . . . , {right arrow over (t_{q})}); S is a matrix that encodes relations between source words and pairs in the bilingual dictionary; T is a matrix that encodes relations between target words and pairs in the bilingual dictionary. 12. The method according to
13. The method according to
(v, w)=Ξ_{s} {right arrow over (v)},Ξ _{t} {right arrow over (w)} ={right arrow over (v)} ^{T}Ξ_{s} ^{T}Ξ_{t} {right arrow over (w)}, where Ξ_{s}=[ξ_{s} ^{1}, . . . ξ_{s} ^{l}]^{T }and Ξ_{t}=[ξ_{t} ^{1}, . . . ξ_{t} ^{l}]^{T}, and ξ_{s }and ξ_{t }denote directions in the source and target vector spaces. 14. The method according to
15. The method according to
(v, w)=K(v, w)=∇l(v)^{T} I _{F} ^{−1} ∇l(w), where l(x)=InP(x|θ) the log-likelihood of vocabulary words x, and I_{F}=E(∇l(x)∇l(y)^{T}) denotes the Fisher information matrix where x and y are any vocabulary word from source and target vocabularies (e_{1}, . . . , e_{m}) and (f_{1}, . . . ,f_{r}) respectively. 16. The method according to
18. The method according to
19. The method according to
20. A method for identifying bilingual pairs in comparable corpora using a bilingual dictionary, comprising:
(a) using the comparable corpora for building for each source word v a context vector {right arrow over (v)}and for each target word w a context vector {right arrow over (w)}; (b) computing source and target context vectors {right arrow over (v)}′ and {right arrow over (v)}′ projected into a sub-space formed by source {right arrow over (s)} and target {right arrow over (t)} bilingual dictionary entry context vectors; and (c) computing a similarity measure between pairs of source words v and target words w using their context vectors {right arrow over (v)}′ and {right arrow over (v)}′ projected to a bilingual space to identify bilingual pairs. 21. The method according to
22. The method according to
23. The method according to
24. A method for identifying bilingual pairs in comparable corpora using a bilingual dictionary, comprising:
(a) building context vectors for source and target words and a number of bilingual dictionary entries using the comparable corpora; (b) computing canonical axes associated with the context vectors of bilingual pairs for defining a mapping from the comparable corpora to canonical subspaces defined by the canonical axes; (c) computing a similarity measure between source and target context vector pairs in a bilingual space defined by their canonical subspaces. 25. A method for identifying bilingual pairs in comparable corpora using a bilingual dictionary, comprising:
(a) building context vectors for source and target words and a number of bilingual dictionary entries using the comparable corpora; (b) computing non-linear latent semantic projections of the context vectors of bilingual pairs for defining a mapping from the comparable corpora to latent semantic subspaces associated with the projections; (c) computing a similarity measure between source and target context vector pairs in a bilingual space defined by their latent semantic subspaces. Description Priority is claimed from U.S. Provisional Application No. 60/586,714, filed Jul. 12, 2004, entitled “Method And Apparatus For Identifying Bilingual Lexicons In Comparable Corpora”, by the same inventors and assignee, which is incorporated herein by reference. The present invention relates generally to methods, and apparatus therefor, for extracting bilingual lexicons from comparable corpora using a bilingual dictionary. Bilingual documents with comparable corpora contain text written in different languages that, as defined herein, refer to a similar topic, but are not translations of each other (i.e., parallel corpora). That is, while corpora that are comparable “talk about the same thing”, corpora that are parallel are direct or mutual translations that maximizes comparability (e.g., as found in a bilingual dictionary). Except for multilingual documents produced by translation for international or government organizations (e.g., parallel product documentation), most multilingual corpora are not parallel but instead comparable (e.g., comparable news stories). However, while few applications produce bilingual lexicons extracted from parallel corpora, many applications require bilingual lexicons. Thus, due to the limited availability of parallel corpora, methods exist for extracting bilingual lexicons from comparable corpora. Some of these known methods of bilingual lexicon extraction from comparable corpora (BLEFCC) are described, for example, in the following publications, which are incorporated herein by reference and hereinafter referred to as the “BLEFCC References”: Rapp, “Identifying Word Translations In Nonparallel Texts”, in Proceedings of the Annual Meeting of the Association for Computational Linguistics, 1995; Peters et al., “Capturing The Comparable: A System For Querying Comparable Text Corpora”, in JADT'95—3rd International Conference on Statistical Analysis of Textual Data, pages 255-262, 1995; Tanaka et al., “Extraction Of Lexical Translations From Non-Aligned Corpora”, in International Conference on Computational Linguistics, COLING'96, 1996; Shahzad et al., “Identifying Translations Of Compound Nouns Using Non-Aligned Corpora”, in Proceedings of the Workshop MAL'99, pages pp. 108-113, 1999; Fung et al., “A Statistical View On Bilingual Lexicon Extraction—From Parallel Corpora To Nonparallel Corpora”, in J. Veronis, editor, Parallel Text Processing, Kluwer Academic Publishers, 2000. Bilingual lexicon extraction from comparable corpora as described in the BLEFCC References relies on the assumption that if two words are mutual translations, then their more frequent collocates, in a broad sense, are likely to be mutual translations as well. Based on this assumption, the approach described in the BLEFCC References for extracting bilingual lexicons from comparable corpora builds context vectors for each target word, translates the target context vectors using a bilingual dictionary, and compares the translation context vector with the target context vector. With these known methods, two problems of “coverage” and “polysemy/synonymy” are known to exist when using a bilingual dictionary to extract bilingual lexicons from comparable corpora. The first problem of coverage occurs when too few corpus words are covered by the bilingual dictionary. However, if the context of the bilingual dictionary is large enough, the method described in the BLEFCC References should contend with the problem of coverage with frequently used words (as opposed to rare words) since it is likely that some context words will belong to the general language. The second problem of polysemy/synonymy associated with the use of bilingual dictionaries to extract bilingual lexicons from comparable corpora arises when dictionary entries have the same meaning (i.e., synonymy) or several meanings (i.e., polysemy), which becomes more significant when only one meaning is represented in the corpus. The method described in the BLEFCC References does not contend well with the polysemy/synonymy problem because all entries on either side of the bilingual dictionary are treated as orthogonal. Similarities with respect to synonyms should preferably not be independent, which the method described in the BLEFCC References does not take into account. As will be seen in more detail below in one geometric embodiment, axes corresponding to two synonyms s_{i }and s_{j }are orthogonal, so that projections of a context vector on synonyms s_{i }and s_{j }will in general be uncorrelated. Consequently, this geometric embodiment provides that a context vector that is similar to synonym s_{i }may not necessarily be similar to synonym s_{j}. Similar to synonymous entries in a bilingual dictionary, similarity with respect to polysemous entries should not be considered independent. For example, the word “bank” in English means either a “financial institution” (having French translation “banque”) or the “ground near a river” (having French translation “berge”). If only the English/French pair bank/banque were to appear in a bilingual dictionary, the method described in the BLEFCC References would consider the English word “river”, which co-occurs with “bank”, similar to the French word “argent” (meaning “money” in English), which co-occurs with “banque” (meaning “financial institution” in French). As the availability of comparable corpora increases (e.g., newspaper articles or patent documents published in different languages), it would be advantageous to provide improved methods for extracting bilingual lexicons from comparable corpora that solves these and other problems. Such improved methods would advantageously optimize the use of existing bilingual dictionaries by, for example, augmenting existing bilingual dictionaries when extracting bilingual lexicons from comparable corpora. Accordingly embodiments of a method, system and article of manufacture therefor, for extracting bilingual lexicons from comparable corpora using a bilingual dictionary are disclosed herein. The embodiments consider the vector space formed by all of the source bilingual dictionary entries (i.e., source words present in a bilingual dictionary), as well as, the vector space formed by all of the target bilingual dictionary entries. In accordance with one aspect of the embodiments, one or more embodiments address the coverage problem described above as it applies to rarer words by bootstrapping the bilingual dictionary by iteratively augmenting it with the most probable translations found in the comparable corpora or corpus. In accordance with another aspect of the embodiments, one or more embodiments address the polysemy/synonymy problem described above by recognizing that context vectors of bilingual dictionary entries provide some additional information with respect to synonymy and polysemy. For synonymy, for example, one or more embodiments recognize that it is likely that the synonyms s_{i }and s_{j }are similar while at the same time context vectors {right arrow over (s_{i})} and {right arrow over (s_{j})} are similar. For polysemy, for example, one or more embodiments recognize that if the context vectors {right arrow over (banque)} and {right arrow over (bank)} have few translation pairs in common, it is likely that “banque” and “bank” are used with somewhat different meanings. In accordance with the embodiments disclosed herein, there is provided a method, apparatus and article of manufacture therefore, for identifying bilingual pairs in comparable corpora using a bilingual dictionary. The method includes: (a) using the comparable corpora to build source context vectors and target context vectors; (b) defining: (i) a source word space with the source context vectors, and (ii) a target word space with the target context vectors; (c) using the bilingual dictionary to project: (i) the source context vectors from the source word space to a source dictionary space, and (ii) the target context vectors from the target word space to a target dictionary space; (d) using the source and target context vectors from the dictionary spaces to identify source/target context vector pairs in a bilingual space; (e) computing a similarity measure for the source/target context vector pairs identified in the bilingual space to identify a bilingual pair. In accordance with additional embodiments disclosed herein, there is provided a method, apparatus and article of manufacture therefore, for identifying bilingual pairs in comparable corpora using a bilingual dictionary. The method does not assume the dictionary space is orthogonal and includes: (a) using the comparable corpora for building for each source word v a context vector {right arrow over (v)} and for each target word w a context vector {right arrow over (w)}; (b) computing source and target context vectors {right arrow over (v)}′ and {right arrow over (w)}′ projected into a sub-space formed by source {right arrow over (s)} and target {right arrow over (t)} bilingual dictionary entry context vectors (where the projected source and target context vectors {right arrow over (v)}′ and {right arrow over (v)}′ include words in the bilingual dictionary that are not present in their corresponding context vectors {right arrow over (v)} and {right arrow over (w)}); and (c) computing a similarity measure between pairs of source words v and target words w using their context vectors {right arrow over (v)}′ and {right arrow over (v)}′ projected to a bilingual space to identify bilingual pairs. In accordance with yet additional embodiments disclosed herein, there is provided a method, apparatus and article of manufacture therefore, for identifying using canonical correlation analysis (CCA) bilingual pairs in comparable corpora using a bilingual dictionary. The method includes: (a) building context vectors for source and target words and a number of bilingual dictionary entries using the comparable corpora; (b) computing canonical axes associated with the context vectors of bilingual pairs for defining a mapping from the comparable corpora to canonical subspaces defined by the canonical axes; (c) computing a similarity measure between source and target context vector pairs in a bilingual space defined by their canonical subspaces. In accordance with yet further additional embodiments disclosed herein, there is provided a method, apparatus and article of manufacture therefore, for identifying using latent semantic analysis (LSA) bilingual pairs in comparable corpora using a bilingual dictionary. The method includes: (a) building context vectors for source and target words and a number of bilingual dictionary entries using the comparable corpora; (b) computing non-linear latent semantic projections of the context vectors of bilingual pairs for defining a mapping from the comparable corpora to latent semantic subspaces associated with the projections; (c) computing a similarity measure between source and target context vector pairs in a bilingual space defined by their latent semantic subspaces. In accordance with the various embodiments, the comparable corpora generated using the embodiments described herein may be used, for example, in applications, such as, cross-language information retrieval, cross-language categorization, bilingual resource development, trans-lingual interference for resource development, and data mining tools that track and translate new terms. Advantageously, such applications would not rely solely on the use of parallel corpora which involves accepting a translation bias inherent to parallel corpora. These and other aspects of the invention will become apparent from the following description read in conjunction with the accompanying drawings wherein the same reference numerals have been applied to like parts and in which: A. Definitions The following terms have the indicated meanings throughout this application, including the claims: A “word” or “term” is used herein to mean any combination of natural language symbols that may, for example, specify a term, word, phrase, or sentence, or any combination or portion thereof. A “lexicon” is used herein to mean a data structure, program, object, or device that indicates words that may occur in a natural language set. A lexicon may be said to “accept” a word it indicates, and those words may thus be called “acceptable” or may be referred to as “in” or “occurring in” the lexicon. In one embodiment, a lexicon is represented using finite state automata. A “bilingual lexicon” is used herein to mean a lexicon that indicates a translation of words: from words in a first natural language to words in a second natural language. In one embodiment, a bilingual lexicon is represented using two-tape finite state automata, where a first language is specified on a first tape and a second language is specified on a second tape of the multi-tape finite state automata (e.g., a bilingual dictionary). In alternate embodiments, multi-tape automata with three or more tapes may be used to carry additional information such as a part-of-speech tag or co-occurring bilingual lexicons. A “measure of association” is used herein to mean a measure of strength of association of words with a word used in context (i.e., a measure of co-occurrence of words, as they may exist in a corpus of documents, with a given word). A “context vector” for a given word is used herein to mean the measure of association of words in context with the given word. The context vector may be a weighted set of “neighbor” words that co-occur in a defined neighborhood of elements (e.g., a corpus of documents), where the weight represents some measure of the co-occurrence strength between the given word and the set of neighbor words. B. Operating Environment for Bilingual Lexicon Extraction The bilingual lexicon extractor 110 uses a geometric view to extract bilingual lexicons using the corpus 112 by developing a source word space 124 and a target word space 125, from source and target context vectors, respectively, developed from the corpus 112. The word spaces 124 and 125 are projected using projections 130 and 132 and bilingual lexicons 114, to produce source and target dictionary space (or subspace) 126 and 127, respectively. Once the subspaces 126 and 127 are aligned with projections 134 and 136 (if necessary) in bilingual subspace 128, pairs of context vectors (one source and one target) are selected and their similarity computed (e.g., using a dot-product or cosine measure). In accordance with one aspect of the embodiments, extended (i.e., additional) bilingual lexicons 117 are added to the bilingual dictionary 114 from the bilingual lexicons identified at 116 to supplement the bilingual lexicons 114. In accordance with another aspect of the embodiments, once produced, the bilingual lexicons identified at 116 may be used with an automated translation system 118, multilingual information retrieval system 120, and cross-lingual categorization system 122, either as bilingual lexicons or bilingual lexicons with associated context information (singly or in combination with bilingual lexicons 114). When used with the translation system 118, the bilingual lexicons may, for example, be used to enrich or tune its existing bilingual resources such as a thesaurus with domain-specific terminology. In another embodiment, the translation system 118 may be used to develop resources through translingual inference. In this embodiment for example, a corpus may be annotated in a first language with a system designed for the first language. Subsequently, the annotations may be mapped to a corpus in a second language to infer a system for the second language, based on the annotations. In such embodiments, translingual inference is enabled with the mapping of annotations which relies on aligning two corpora at the word level. The multilingual information retrieval system 120 operates, for example, by querying in one language and retrieving results in multiple languages. In one embodiment, this is accomplished by translating query terms, where bilingual lexicons are used to search multilingual collections. The cross-lingual categorization system 122 operates, for example, by training its categorizer in one language and categorizing in multiple languages. In one embodiment, this training is accomplished using bilingual lexicons adapted to the content and/or structure of the categorizer. At 206, subspaces 126 and 127 are developed for the source word space 124 and target word space 125 using an initial (or augmented) set of bilingual lexicons (as shown at 114 in In addition to the action performed in In accordance with the various embodiments disclosed herein, the set of pairs identified in context using the context vector space representation, at 208, is performed using different methods for computing the similarity between words in the source language and words the target language, are described in detail below in Section C, D, and E. Such methods for computing similarity may be used singly or in combination are described below in Section F. In one embodiment, context vectors are defined by computing a mutual information association measure (e.g., using a loglikelihood test, disclosed for example by Dunning, in “Accurate Methods For The Statistics Of Surprise And Coincidence”, Computational Linguistics, 19(1):64-74, 1993, which is incorporated herein by reference). The mutual information association measure may, for example, be measured between terms occurring in the same context window of a predetermined size (e.g., by considering a neighborhood of plus or minus two words around the current word) that is summed over all contexts of the corpora. It will be appreciated, however, that alternate association measures and context sizes may be used to compute context vectors. Once the context vectors are computed, memory and computational constraints of the system may require pruning of the context vectors. For example, pruning in one embodiment involves pruning contexts vectors computed for a corpus such that, for each term, the components of a context vector after pruning represent a large percentage (e.g., ninety percent) of the total information measured (i.e., the total information in the original context vector before pruning). In another embodiment, pruning involves pruning from a context vector all but the top N ranked components that hold the most mutual information measured. In either embodiment, after pruning, the context vectors may, in addition, be normalized so that their Euclidean norm is equal to one. C. Computing Similarity Using Context Vectors This section describes two approaches for extracting bilingual lexicons from comparable corpora that involve computing similarity between words in a source language and a target language using a context vector of bilingual dictionary entries. Each approach is presented geometrically, the first of which makes reference to the BLEFCC References (which is referred to herein as the “Standard Approach” or “Standard Method”), and the second of which extends the Standard Approach (which is referred to herein as the “Extended Approach”). C.1 The Standard Approach As set forth above, one assumption made in the Standard Approach is that if two words are mutual translations then their more frequent collocates are likely to be mutual translations as well. Based on this assumption, the Standard Approach builds context vectors for each source and target word, translates the target context vector using a bilingual dictionary, and compares the translation with the source context vector. Geometrically, the Standard Approach is based on the projection of context vectors onto a dictionary. This approach assumes that two terms are in translational relationship (i.e., bilingual pairs) if their context vectors projected onto the dictionary entries are translations of each other. One embodiment for carrying out the Standard Approach may be depicted by the following set of operations: (1) using a comparable corpus, for each source word v build a context vector {right arrow over (v)} consisting of the measure of association “a(v,e)” of each word “e” in the context of “v”, and for each target word “w” build a context vector “{right arrow over (w)}” consisting of the measure of association “a(w,f)” of each word “f” in the context of “w”; (2) translate the target context vectors {right arrow over (w)} with a general bilingual dictionary “ ”, while accumulating the contributions from words that yield identical translations; (3) compute the similarity between source word v and target word w using a similarity measure, such as, the Dice or Jaccard coefficients, or the Cosine measure. For more background relating to the computation of distance metrics see “Foundations of Statistical Natural Language Processing” by Manning and Schutze, MIT Press, 1999, which is incorporated herein by reference. By observing that the dot-product contributes to measures of similarity of the Standard Method, the similarity of the Standard Method may be given by the following dot-product between source context vector {right arrow over (v)} and the translation “{right arrow over (tr(w))}” of the target context vector {right arrow over (w)}:
It will be appreciated by those skilled in the art that the approach presented in equation [1] (as well as other disclosed below) for computing the dot-product (or similarity measure between a source/target pair) requires some general bilingual dictionary as initial seed. One way to circumvent this requirement involves automatically building a seed lexicon based on spelling and cognate clues, as disclosed by Koehn et al., in “Learning A Translation Lexicon From Monolingual Corpora”, ACL 2002 Workshop on Unsupervised Lexical Acquisition, 2002, which is hereby incorporated herein by reference. Another approach directly addresses the problem by initially searching for a translation mapping which optimally preserves the intra-lingual association measure between words, as disclosed by Diab et al., in “A Statistical Word-level Translation Model For Comparable Corpora”, Proceeding of the Conference on Content-Based Multimedia Information Access (RIAO) 2000, which is hereby incorporated herein by reference. In Diab, the underlying assumption is that pairs of words which are highly associated in one language should have translations that are highly associated in the other language. In the approach described by Diab, the association measure is defined as the Spearman rank order correlation between their context vectors restricted to “peripheral tokens” (i.e., highly frequent words). This search method is based on a gradient decent algorithm that iteratively changes the mapping of a single word until (locally) minimizing the sum of squared differences between the association measure of all pairs of words in one language and the association measure of the pairs of translated words obtained by the current mapping. The association measures a(v,e) and a(w,f) may be viewed, respectively, as the coordinates of the m-dimensional context vector {right arrow over (v)} in the vector space formed by the orthogonal basis (e_{1}, . . . , e_{m}) (as shown in As the p×q matrix M encodes the relationship between the source and target words s and t (or entries) in the bilingual dictionary , equation [1] may be rewritten such that the similarity (v, w) between a source entry v and a target entry w is given by the dot-product context vector {right arrow over (v)} and the translation of the context vector {right arrow over (w)}:(v, w)= {right arrow over (v)}, {right arrow over ( tr(w))}=(P _{s} {right arrow over (v)})^{T} M(P _{t} {right arrow over (w)}), [2] where “T” denotes transpose (here and elsewhere herein). In addition, the bilingual dictionary may be rewritten into subparts such that the matrix M may be rewritten as S^{T}T, with S an n×p matrix and T an n×q matrix that each encode relations between words and pairs in the bilingual dictionary (e.g., S_{ki}=1 iff s_{i }is in the k^{th }translation pair). Hence, the similarity (v, w) may be given by: (v, w)={right arrow over (v)} ^{T} P _{s} ^{T} S ^{T} TP _{t} {right arrow over (w)}= SP _{s} {right arrow over (v)}, TP _{t} {right arrow over (w)}, [3] which shows that the Standard Approach amounts to performing the dot-product in the vector space 318 formed by the n pairs ((s_{1}, t_{l}), . . . , (s_{p}, t_{k})) (from the projection, at 314, of the matrix S on the sub-space 310 and the projection, at 316, of the matrix T on the sub-space 312). Because a given word almost never co-occurs with itself (i.e., appears as an entry in its own context vector), it is added to its own context vector, in one embodiment, with a high co-occurrence score (while in alternate embodiments other co-occurrence scoring levels may be used). The n pairs ((s_{1}, t_{l}), . . . , (s_{p}, t_{k})) in the vector space 318 are assumed to be orthogonal, and correspond to translation pairs. C.2 Extended Approach Geometrically, the Extended Approach is based on the similarity of context vectors with dictionary entries. This approach assumes that two terms are in translational relationship (i.e., bilingual pairs) if their context vectors are similar to the context vectors of dictionary entries that are translations of each other. That is, given that synonyms may be captured through similarity of context vectors, the projections made in the Standard Approach are replaced in this embodiment with a mapping into the sub-space formed by the source and target context vectors of the dictionary entries. Accordingly, this embodiment does not assume the dictionary space 310 and 312, shown in More specifically, instead of projecting the source context vector v on the sub-space 310 formed by (s_{1}, . . . , s_{p}) and the target context vector {right arrow over (w)} on the sub-space 312 formed by (f_{1}, . . . , f_{r}) shown in Figure, this embodiment uses a p×m projection matrix Q_{s }(at 402) to map the context vector {right arrow over (v)} on the sub-space 406 generated by ({right arrow over (s_{1})}, . . . , {right arrow over (s_{p})}), and a p×m projection matrix Q_{r }(at 404) to map the context vector {right arrow over (w)} on the sub-space 408 generated by ({right arrow over (t_{1})}, . . . , {right arrow over (t_{q})}). With this improved mapping given by Q_{t }and Q_{s}, a vector space in which synonymous dictionary entries are close to each other is generated. Thus, if the target word context vector {right arrow over (v)} (as defined in comparable corpus space) is close to the target dictionary entry context vectors {right arrow over (s_{i})} and {right arrow over (s_{j})} (as defined in the comparable corpus space), and s_{i }and s_{j }are synonyms, then the translations of both s_{i }and s_{j }will be used to find those words w close to v (i.e., co-occur with). Hence with this improved mapping Q_{t }and Q_{s}, the similarity (v, w) may be given in this embodiment by:(v, w)= SQ _{s} {right arrow over (v)}, TQ _{t} {right arrow over (w)} ={right arrow over (v)} ^{T} Q _{s} ^{T} S ^{T} TQ _{t} {right arrow over (w)}, [4] where, in one embodiment, the mapping Q_{s }is given by the following m×p matrix: and the mapping Q_{t }is given by the following r×q matrix: where e_{i }is a source entry and f_{j }is a target entry in the bilingual dictionary and s_{i }is a source word and t_{j }is a target word in the comparable corpora. In this embodiment, noise may result from spurious relationships introduced when dictionary words not present in the context vector of a given word are used to translate the given word since most bilingual dictionary entries may be represented in the resulting source {right arrow over (v)}′ and target {right arrow over (w)}′ context vectors after projecting the source {right arrow over (v)} and target {right arrow over (w)} context vectors with Q_{s }at 402 and Q_{t }at 404, respectively. One embodiment accounts for the possibility of such noise being introduced by restricting (i.e., pruning) the number of translation pairs in the bilingual dictionary to only those N dictionary entries (e.g., N=200) closest to the source {right arrow over (v)} and target {right arrow over (w)} context vectors (i.e., based on the measure of similarity between the source {right arrow over (v)} and target {right arrow over (w)} context vectors and each source {right arrow over (s)} and target {right arrow over (t)} bilingual dictionary entry context vectors). Such pruning permits spurious relationships to be discarded by selecting only those translation pairs that are in true relation with the word to be translated. C.3 Alternate Embodiments To Extended Approach In alternate embodiments, the mapping Q_{s }and Q_{t }given at 402 and 404, respectively, may be given by the pseudo-inverse of R_{s }and R_{t}. It will be appreciated by those skilled in the art, however, that computing the pseudo-inverse of R_{s }and R_{t }is a complex operation, while the preceding embodiment is a less complex operation because the columns of the Q matrices correspond to the context vectors of the bilingual dictionary . As set forth below, this method generalizes over the probabilistic approach presented by Dejean et al., in “An Approach Based On Multilingual Thesauri And Model Combination For Bilingual Lexicon Extraction”, International Conference On Computational Linguistics, COLING, 2002, which is incorporated herein by reference (hereinafter referred to as the “Dejean Reference”).More specifically, as set forth in Section C.2 above, SQ_{s}{right arrow over (v)}, is an n-dimensional vector, defined over ((s_{1}, t_{l}), . . . , (s_{p}, t_{k})). The coordinate of SQ_{s}{right arrow over (v)} on the axis corresponding to the translation pair (s_{i}, t_{j}) is {right arrow over (s_{i})}, {right arrow over (v)}, and the coordinate of TQ_{t}{right arrow over (w)} on the same axis is {right arrow over (t_{j})}, {right arrow over (w)}. Thus, the similarity (v, w) given by equation [4] above can be rewritten as:which can be normalized in order to acquire a probability distribution leading to similarity (v, w) given by: By imposing probability P(t_{j}) to be uniform, and by denoting C to be a translation pair, similarity (v, w) may be defined as: with the interpretation that only the source word and the target word in C are relevant for probabilities P(C|v) and P(w|C), respectively. To identify those words w closest to a given word v, similarity (v, w) may be defined as: which is similar to the probabilistic model adopted in the Dejean Reference. It will be appreciated by those skilled in the art that this probabilistic model is a special case of the Extended Approach set forth in Section C.2 above. D. Computing Similarity Using Canonical Correlation Analysis In this embodiment, two terms are considered to have a translation relationship if their context vectors projected in a space of language-independent latent semantics are similar to each other. This language-independent latent semantics space and the associated projections from the source and target languages are determined by Canonical Correlation Analysis (CCA). CCA simultaneously offers the benefits of dimension reduction (e.g., to cope with synonymy issues) and the automatic extraction of axes of maximal correlation between the two languages, which can be considered as the manifestations of the same phenomenon (semantics). One embodiment for carrying out this approach may be depicted by the following set of operations: (a) building context vectors for source and target words and all (or a defined number of) bilingual dictionary entries using the comparable corpora (this permits dictionary entries to be accounted even if they are not present in source/target context vectors); (b) computing canonical axes associated with the context vectors of the source and target words for adapting the mapping 302/304 defined by the bilingual dictionary to the comparable corpora in their canonical subspaces 502/504; (c) computing similarity in the bilingual space 506 between source and target word pairs. Formally in this embodiment, the similarity (v, w) between the source and target context vectors {right arrow over (v)} and {right arrow over (w)}, which forms the basis of the bilingual lexicon extracted by this third embodiment, may be given by:(v, w)=Ξ_{s} {right arrow over (v)},Ξ _{t} {right arrow over (w)} ={right arrow over (v)} ^{T}Ξ_{s} ^{T}Ξ_{t} {right arrow over (w)}, [5] where Ξ_{s}=[ξ_{s} ^{1}, . . . ξ_{s} ^{1}]^{T }and Ξ_{t}=[ξ_{t} ^{1}, . . . ξ_{t} ^{1}]^{T}, and where the ξ_{s }and ξ_{t }denote the directions in the source and target vector spaces (defined by orthogonal basis (e_{1}, . . . , e_{m}) and (f_{1}, . . . f_{r})) such that the correlation of the projections of the translation pairs on these directions is maximized. To derive Ξ_{s }and Ξ_{t}, the general bilingual dictionary is used to “pair” observations, where each observation is the source and target context vectors {right arrow over (v)} and {right arrow over (w)}. If the source entry has more than one translation, there are as many observations for this entry as the number of its translations in the general bilingual dictionary . Similar to other embodiments, the general bilingual dictionary may be either binary or a weight matrix.Given the observations (the source and target context vectors {right arrow over (v)} and {right arrow over (w)}) and the vectors ξ_{s }and ξ_{t}, the following matrix may be defined:The size of this matrix is n×(m+r), where the rows of the matrix correspond to translation pairs (s_{i}, t_{j}), where the notation (s^{(k)}, t^{(k)}) is a renumbering of (s_{i}, t_{j}), and the columns of the matrix correspond to source and target vocabularies (e_{1}, . . . , e_{m}) and (f_{1}, . . . , f_{r}) in the comparable corpora, respectively. In an alternate embodiment, the observations defined by the source and target context vectors {right arrow over (v)} and {right arrow over (v)} are restricted to the terms in the bilingual dictionary by simple projection.The matrix shows that each translation pair supports two views, provided by the context vectors in the source and target languages. Each view is connected to the other by the translation pair it represents. The statistical technique of Canonical Correlation Analysis can be used to identify directions ξ_{s }and ξ_{t }in the source view (first m columns of matrix ) and target view (last r columns of matrix ) that are maximally correlated (i.e., behave the same way with respect to the translation pairs), respectively. Intuitively, the directions in the source and target vector spaces ξ_{s }and ξ_{t }define latent semantic axes that capture the implicit relations between translation pairs, and induce a natural mapping across languages, which may be formulated as the maxima given by:As in principal component analysis, once the first two directions (ξ_{s} ^{1}, ξ_{t} ^{1}) have been identified, the process can be repeated in the sub-space orthogonal to the one formed by the directions already identified. However, a general solution based on a set of eigenvalues is possible, where weighted combinations of terms designated by the m-dimensional vector ξ_{s }in the source language and the r-dimensional vector ξ_{t }in the target language are identified such that the projections defined by the vectors ξ_{s }and ξ_{t }maximize the correlation within the observations (i.e., the source and target context vectors {right arrow over (v)} and {right arrow over (w)}). The general solution based on eigenvalues can be formulated as the following generalized eigenvalue problem:
The standard approach to solve the eigenvalue problem defined by equation [6] above is to perform an incomplete Cholesky decomposition of a regularized form of D, as disclosed by Bach et al., in “Kernel Independent Component Analysis”, Journal of Machine Learning, 2001, which is incorporated herein by reference. Using incomplete Cholesky decomposition of a regularized form of D to solve the eigenvalue problem defined by equation [6], yields pairs of source and target directions (ξ_{s} ^{1},ξ_{t} ^{1}), . . . , (ξ_{s} ^{1},ξ_{t} ^{1}) that define a new bilingual subspace 506 (where the source and target context vectors {right arrow over (v)}″and {right arrow over (w)}″ are linear projections of {right arrow over (v)} and {right arrow over (w)}, respectively), shown in It will be appreciated by those skilled in the art that the number l of vectors retained in Ξ_{s}=[ξ_{s} ^{1}, . . . ξ_{s} ^{l}]^{T }and Ξ_{t}=[ξ_{t} ^{1}, . . . ξ_{t} ^{l}]^{T }of each language directly defines the dimensions of the bilingual subspace 506 used for comparing words across language. In one embodiment, the number of dimensions that are used in the computation is empirically optimized (e.g., l=300). Further, those skilled in the art will appreciate that CCA and its kernelised version (used by Vinokourov et al., in “Finding Language-Independent Semantic Representations of Text Using Kernel Canonical Correlation Analysis”, Advances in Neural Information Processing Systems 12, 2002, which is incorporated herein by reference, as a way to build a cross-language information retrieval system from parallel corpora) may be used to infer language-independent semantic representations from comparable corpora, which induce a similarity between words in the source and target languages. E. Computing Similarity Using PLSA In this embodiment, the matrix (defined in section D above) is arranged such that synonyms of translation pairs appear in similar clusters while polysemous words of translation pairs appear in different clusters. Similar to the other embodiments, two terms are considered to have a translation relationship if their context vectors projected in a common space are similar to each other. However, in this embodiment PLSA is used to identify structure in the matrix C in order to facilitate the identification of translation relationships. More background on PLSA is disclosed by Hofmann, in “Probabilistic Latent Semantic Analysis”, Proceedings of the Fifteenth Conference on Uncertainty in Artificial Intelligence, pages 289-296, 1999, and Deerwester et al., in “Indexing By Latent Semantic Analysis”, Journal of the American Society for Information Science, 41 (6):391-407, 1990, which are both incorporated herein by reference.More specifically in this embodiment, the matrix encodes in each row k the context vectors of the source (first m columns) and the target (last r columns) of each translation pair. In accordance with this embodiment, the content of the matrix is clustered using PLSA so that translation pairs with synonymous words appear in the same cluster, while translation pairs with polysemous words appear in different clusters (i.e., soft clustering). Further, it is desirable that the clustering of the content of the matrix behaves symmetrically with respect to translation pairs and vocabulary words because of the symmetry between the roles played by translation pairs and vocabulary words.Assuming the matrix encodes the co-occurrences between vocabulary words x and translation pairs d, the measure of association a(s_{i}, e_{j}), in this embodiment, is the frequency of occurrence (or number of occurrences) of ej in the context of s_{i }and f_{j }in the context of t_{i}. In one implementation of this embodiment, PLSA may be used to model the probability of co-occurrence x and d via latent classes α using:where, for a given class, words and translation pairs are assumed to be independently generated from class-conditional probabilities P(x|α) and P(d|α). Note that the latter probability distribution is language-independent, and that the same latent classes are used for the two languages. The parameters of the model are obtained by maximizing the likelihood of the observed data (matrix ) through Expectation-Maximization, which is disclosed by Dempster et al., “Maximum Likelihood From Incomplete Data Via The EM Algorithm”, Journal of the Royal Statistical Society, Series B, 39(1):1-38, 1977, which is incorporated herein by reference. In addition, in order to reduce the sensitivity to initial conditions, a deterministic annealing scheme is used as disclosed by Ueda et al., in “Deterministic Annealing Variant Of The EM Algorithm”, Advances in Neural Information Processing System 7, pages 545-552, 1995, which is incorporated herein by reference. The deterministic annealing EM algorithm disclosed by Hofmann for PLSA cited above leads to the following equations for iteration t and deterministic annealing parameter β:
While this method of clustering the content of the matrix using PLSA may identify relevant bilingual semantic classes, it does not directly define a similarity between words across languages. The similarity between words across languages (i.e., associated similarities) may be defined using Fisher kernels, as disclosed by Jaakkola et al., in “Exploiting Generative Models In Discriminative Classifiers”, Advances in Neural Information Processing Systems 11, pages 487-493, 1999, which is incorporated herein by reference.Fisher kernels may be used to derive a similarity measure from a probabilistic model, and are useful whenever a direct similarity between observed features is hard to define or insufficiently defined. In one embodiment, denoting l(x)=InP(x|θ) the log-likelihood of vocabulary words x the similarity (v, w) may be defined using the Fisher kernel as:(v, w)=K(v, w)=∇l(v)^{T} I _{F} ^{−1} ∇l(w), where the Fisher information matrix I_{F}=E(∇l(x)∇l(y)^{T}) keeps the kernel independent of reparameterization, and where x and y are any vocabulary word from source and target vocabularies (e_{1}, . . . , e_{m}) and (f_{1}, . . . , f_{r}), respectively. It is assumed with a suitable parameterization that I_{F}≈1. Using PLSA as disclosed by Hofmann, in “Learning The Similarity Of Documents: An Information-Geometric Approach To Document Retrieval And Categorization”, Advances in Neural Information Processing Systems 12, page 914, MIT Press, 2000, which is incorporated herein by reference, the Fisher kernel between two words v and w becomes: where d ranges over the translation pairs. The Fisher kernel performs the dot-product in a vector space defined by the parameters of the model. With only one class, the expression of the Fisher kernel reduces to: Those skilled in the art will appreciate that apart from the additional intercept (“1”), this computation of similarity (v, w) may be defined similar to the similarity provided by the Standard Approach set forth in Section B.1 above, with associations given by scaled empirical frequencies a(x,d)={circumflex over (P)}(d|x)/√{square root over (P(d))}) for vocabulary words x and translation pairs d. Accordingly, the Standard Approach and the Fisher kernel with one class would be expected to have similar behavior. In addition to the Fisher kernel set forth above, two alternate versions may be obtained through normalization (NFK) and exponentiation (EFK), respectively, as:F. Combination Of Methods In another embodiment, methods for computing similarity (v, w) described above are combined to compute an overall similarity value to improve the average precision of the various bilingual lexicon extraction methods. Various methods for combining similarity computations may be used. For example, an overall similarity score may be computed using a percentage of each score. The percentage attributed to each computed similarity score in the overall score need not be equal but may instead be fixed or vary depending on, for example, performance data.In combining similarity computation methods, the overall similarity score may be computed over a series of stages, where each stage is computed using a different similarity measure. For instance, the first stage may compute a first set of similarities and the second stage may compute a second set of similarities using the highest results of the first stage, where the final result is the highest similarities of the second stage. That is, values of similarity that are candidate bilingual lexicons from the first stage may be re-ranked during one or more additional stages using alternate similarity measures. In yet another example, such a combination of methods involves combining Fisher kernels with different latent classes in a first stage, and a combination of the different methods in a second stage. G. Miscellaneous Additional background concerning the embodiments described herein is published by Gaussier et al., in “A Geometric View On Bilingual Lexicon Extraction From Comparable Corpora”, published in 42nd Annual Meeting of the Association for Computational Linguistics (ACL) Jul. 21-26, 2004 Barcelona, Spain, which is incorporated herein by reference. Those skilled in the art will recognize that a general purpose computer may be used for implementing the operating environment shown in Further, those skilled in the art will recognize that the forgoing embodiments may be implemented as a machine (or system), process (or method), or article of manufacture by using standard programming and/or engineering techniques to produce programming software, firmware, hardware, or any combination thereof. It will be appreciated by those skilled in the art that the flow diagrams described in the specification are meant to provide an understanding of different possible embodiments. As such, alternative ordering of the steps, performing one or more steps in parallel, and/or performing additional or fewer steps may be done in alternative embodiments. Any resulting program(s), having computer-readable program code, may be embodied within one or more computer-usable media such as memory devices or transmitting devices, thereby making a computer program product or article of manufacture according to the embodiment described herein. As such, the terms “article of manufacture” and “computer program product” as used herein are intended to encompass a computer program existent (permanently, temporarily, or transitorily) on any computer-usable medium such as on any memory device or in any transmitting device. Executing program code directly from one medium, storing program code onto a medium, copying the code from one medium to another medium, transmitting the code using a transmitting device, or other equivalent acts may involve the use of a memory or transmitting device which only embodies program code transitorily as a preliminary or final step in making, using, or selling the embodiments as set forth in the claims. Memory devices include, but are not limited to, fixed (hard) disk drives, floppy disks (or diskettes), optical disks, magnetic tape, semiconductor memories such as RAM, ROM, Proms, etc. Transmitting devices include, but are not limited to, the Internet, intranets, electronic bulletin board and message/note exchanges, telephone/modem based network communication, hard-wired/cabled communication network, cellular communication, radio wave communication, satellite communication, and other stationary or mobile network systems/communication links. A machine embodying the embodiments may involve one or more processing systems including, but not limited to, CPU, memory/storage devices, communication links, communication/transmitting devices, servers, I/O devices, or any subcomponents or individual parts of one or more processing systems, including software, firmware, hardware, or any combination or subcombination thereof, which embody the invention as set forth in the claims. While particular embodiments have been described, alternatives, modifications, variations, improvements, and substantial equivalents that are or may be presently unforeseen may arise to applicants or others skilled in the art. Accordingly, the appended claims as filed and as they may be amended are intended to embrace all such alternatives, modifications variations, improvements, and substantial equivalents. Referenced by
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